Add and subtract mixed numbers: word problems

Learning Objectives Translate word problems involving congruent figures into mathematical expressions with mixed numbers. Calculate the perimeter of polygons whose side lengths are given as mixed numbers. Determine an unknown side length of a figure by applying the properties of congruence and mixed number subtraction. Solve multi-step problems requiring both addition and subtraction of mixed numbers in a geometric context. Verify calculations by converting mixed numbers to improper fractions and performing the operations. Interpret geometric diagrams to formulate equations involving mixed numbers. How does a structural engineer calculate the total length of steel needed for two congruent triangular trusses if the side lengths are 8 1/4 ft, 15 7/8 ft, and 15 7/8 ft? 🏗️ Whil...

TermDefinitionExample Mixed NumberA number consisting of a whole number and a proper fraction.The length of a side of a triangle is 5 3/4 inches. Improper FractionA fraction in which the numerator is greater than or equal to the denominator. Mixed numbers are often converted to improper fractions for easier calculation.The mixed number 5 3/4 is equivalent to the improper fraction 23/4. Congruent FiguresFigures that have the exact same size and shape. All corresponding sides and corresponding angles are equal.If Triangle ABC ≅ Triangle XYZ, then the length of side AB is equal to the length of side XY. Corresponding PartsThe sides or angles of congruent figures that are in the same relative position.In two congruent pentagons, the shortest side of the first pentagon corresponds to the short...

Addition of Mixed Numbers A \frac{b}{c} + D \frac{e}{f} = (A + D) + (\frac{b}{c} + \frac{e}{f}) Add the whole numbers and the fractions separately. If the resulting fraction is improper, convert it to a mixed number and add its whole part to the total. Subtraction of Mixed Numbers (Regrouping) If \frac{b}{c} < \frac{e}{f}, then A \frac{b}{c} = (A-1) + \frac{b+c}{c} When subtracting, if the first fraction is smaller than the second, you must 'borrow' or 'regroup' 1 from the whole number. The borrowed 1 is expressed as a fraction (c/c) and added to the existing fraction before subtracting. Conversion to Improper Fractions A \frac{b}{c} = \frac{A \times c + b}{c} An alternative method for both addition and subtraction is to convert all mixed numbe...